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The search engines follow the <a href= - as said by Duckula.
So SE's will find your pages even if the only links are from graphics.
The second consideration is that SE's determine what your page is about by a number of factors including page content, titles and link text. So linking with text gives your page extra weight for that phrase.
If you have a graphical menu use the alt text on the image - I have no proof but think that SE's will count this text (less than with plain text but every little helps).
Additionally a footer with plain text links will help - it maintains a good internal linking structure, gives the SE's plain text to use. It also becomes useful to many web surfers who instinctively visit the bottom of pages for certain info - like contact details, sitemap etc.
So in summary - it's not necessary but helps.